1. Field of the Invention
The present invention generally relates to imperceptible watermarking of images and, more particularly, to watermarking implemented on the compressed version of an image in a way that allows the usage of public key cryptography.
2. Background Description
The image to be watermarked is assumed to be in digital form. An imperceptible watermark (hereafter watermark for short) is defined as an alteration of the data set which is mostly not perceptible to a human, but can be recognized by a machine such as a computer. Otherwise, the watermark should be (mostly) invisible. The general principle of such a watermark has been disclosed, for instance, in "Digital Watermarking for High-quality Imaging", by M. M. Yeung, F. C. Mintzer, G. W. Braudaway, and A. R. Rao, Proceedings of the IEEE Signal Processing Society Multimedia Workshop, Princeton, N.J., 1997. Here we are interested in fragile watermarks, by which we mean watermarks which allow the recognition that an image is authentic and has not been altered, rather that in robust watermarks which are mainly devoted to establish ownership. Such fragile watermark schemes already exist with several virtues as for example in copending U.S. patent application Ser. No. 09/059,498 to D. Coppersmith, F Mintzer, C. Tresser, C. W. Wu, and M. M. Yeung, filed Apr. 13, 1998 and entitled "Secured Signal Modification and Verification with Privacy Control". Here we are interested in a fragile watermark scheme which is compatible with image compression. The discussion will be organized around JPEG compressed images, as described in JPEG Still Image Compression Standard by W. B. Pennebaker and J. L. Mitchell published by Van Nostrand Reinhold, New York, 1993. However, anybody versed in the art of computer imaging would readily understand how to adapt this invention to other compression schemes as long as the least visible information content can be extracted and modified. The choice we have made is motivated by the fact that JPEG is a widely accepted International standard for image compression.
A digitized color image could be thought of as a single n.sub.1.times.n.sub.2.times.N array with N.ltoreq.3. Here, the picture is supposed to be rectangular with n.sub.1, pixels in the horizontal direction, n.sub.2 pixels in the vertical direction, and 3 is the minimal number of components for a color image.
Similarly, a digitized gray-scale image could be thought of as a single n.sub.1.times.n.sub.2 array. The description of an embodiment of the invention focuses on gray-scale images; however, the invention is readily applicable to other data sets in more general sense, so that the word "image" could be replaced by any other human perceptible data sets such as color images or video. For definiteness, we will assume in the sequel that n.sub.1 =n.sub.2 =512, but more general cases would be treated by an obvious adaptation of what will be presented here. In particular, the essential invisibility of the artifacts generated by this invention should result in even less visibility for color image than for grey-scale images.